11) A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.
Let l and bare the length and breadth of rectangle respectively and r will be the radius of circle
The total perimeter of window = perimeter of rectangle + perimeter of the semicircle
Area of window id given by (A) =
Hence, b = 5/2 is the point of maxima
Hence, these are the dimensions of the window to admit maximum light through the whole opening